An electromechanical system in one example measures a parameter. The electromechanical system may comprise a micro-electromechanical system (“MEMS”) accelerometer or gyroscope that measures the parameter. For example, the accelerometer measures an acceleration and the gyroscope measures an angular rate (e.g., rotation). The gyroscope in one example comprises a vibrating ring with high Q degenerate fundamental modes of vibration. For example, high Q vibrating rings require little energy to sustain vibration. The vibrating ring in one example is employable for high performance closed loop angular rate sensing. The vibrating ring in another example is employable for lower performance open loop angular rate sensing. The mathematical model of the symmetrical vibrating ring is in many aspects similar to a vibrating ring or hemispherical resonator gyroscope (“HRG”). The analytical similarity to the hemispherical resonator gyroscope indicates that the vibrating ring gyroscope has the potential of achieving similar performance.
Drive components coupled with the vibrating ring cause a first oscillation of the vibrating ring. An angular rate of the vibrating ring and the first oscillation induce a Coriolis force on the vibrating ring. For example, the angular rate is about the longitudinal axis of the vibrating ring. The Coriolis force causes a second oscillation of the vibrating ring. The second oscillation is substantially perpendicular to the first oscillation. Feedback components in one example provide feedback on a magnitude of the first oscillation to the drive components for regulation of the first oscillation. Pickoff sensor components sense the second oscillations and apply control signals to null the pickoff signal. The control signals are a measure of the magnitude and polarity of the angular rate of the vibrating ring.
Small, low cost, low power navigation-grade inertial systems are needed to enable new applications such as personal navigation of individual soldiers and the guidance and control of air, ground and under water autonomous vehicles in GPS denied environments. Micro-electromechanical systems inertial systems are currently in development that promise to provide small, low cost, low power inertial systems for tactical grade applications such as guided munitions. Current tactical-grade MEMS inertial systems have gyro bias uncertainty in the range of 20-50 degrees per hour and angle random walk of 0.02 degrees per root hour. Future, small, low cost, low power navigation-grade inertial systems require lower gyro bias uncertainty and angle random walk.
Currently, a manufacturer of inertial sensors performs calibration of the inertial sensors with thermal modeling at a system level. The inertial system performance may be limited by one or more of: instability of the inertial sensors' bias and scale factor, non-repeatability of the thermal model, or hysteretic and thermal gradient induced errors that can not be modeled.